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make the two multiply consistent so they easier to read and compare
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edit approved Jan 8, 2014 at 2:51
wjl
edit approved Jan 8, 2014 at 2:51
wjl
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In computer graphics, we use matrices to encode transformations.

Matrices that contain only translation, rotation or scaling transforms have a commonly-exploited interpretation: the upper-left 3x3 of the matrix contains only rotation or scale data, the bottom row or right column contains translation data. This is not a generality, but holds true often enough for the subset of transformations represented in computer graphics that people make use of it.

There is, similarly, a relationship between the values of the matrix and the corresponding coordinate frame the matrix represents (which is not always "world space," I should note). The upper-left 3x3 columns (or rows) represent the X, Y and Z axes of the coordinate frame.

Whether or not the rows represent axes or the column do depends on whether you are using the convention of multiplying as row vector * matrix or matrix times* column vector. When performing matrix multiplication, the inner dimensions of the two matrices must agree, and so whether you are representing vectors as row matrices or column matrices impacts that choice (OpenGL and traditional math tend to prefer column vectors).

I recommend getting a good book on linear algebra, or at least taking a look at the Matrix and Quaternion FAQ and this post on matrix layouts in DirectX and OpenGL.

In computer graphics, we use matrices to encode transformations.

Matrices that contain only translation, rotation or scaling transforms have a commonly-exploited interpretation: the upper-left 3x3 of the matrix contains only rotation or scale data, the bottom row or right column contains translation data. This is not a generality, but holds true often enough for the subset of transformations represented in computer graphics that people make use of it.

There is, similarly, a relationship between the values of the matrix and the corresponding coordinate frame the matrix represents (which is not always "world space," I should note). The upper-left 3x3 columns (or rows) represent the X, Y and Z axes of the coordinate frame.

Whether or not the rows represent axes or the column do depends on whether you are using the convention of multiplying as row vector * matrix or matrix times column vector. When performing matrix multiplication, the inner dimensions of the two matrices must agree, and so whether you are representing vectors as row matrices or column matrices impacts that choice (OpenGL and traditional math tend to prefer column vectors).

I recommend getting a good book on linear algebra, or at least taking a look at the Matrix and Quaternion FAQ and this post on matrix layouts in DirectX and OpenGL.

In computer graphics, we use matrices to encode transformations.

Matrices that contain only translation, rotation or scaling transforms have a commonly-exploited interpretation: the upper-left 3x3 of the matrix contains only rotation or scale data, the bottom row or right column contains translation data. This is not a generality, but holds true often enough for the subset of transformations represented in computer graphics that people make use of it.

There is, similarly, a relationship between the values of the matrix and the corresponding coordinate frame the matrix represents (which is not always "world space," I should note). The upper-left 3x3 columns (or rows) represent the X, Y and Z axes of the coordinate frame.

Whether or not the rows represent axes or the column do depends on whether you are using the convention of multiplying as row vector * matrix or matrix * column vector. When performing matrix multiplication, the inner dimensions of the two matrices must agree, and so whether you are representing vectors as row matrices or column matrices impacts that choice (OpenGL and traditional math tend to prefer column vectors).

I recommend getting a good book on linear algebra, or at least taking a look at the Matrix and Quaternion FAQ and this post on matrix layouts in DirectX and OpenGL.

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user1430
user1430

In computer graphics, we use matrices to encode transformations.

Matrices that contain only translation, rotation or scaling transforms have a commonly-exploited interpretation: the upper-left 3x3 of the matrix contains only rotation or scale data, the bottom row or right column contains translation data. This is not a generality, but holds true often enough for the subset of transformations represented in computer graphics that people make use of it.

There is, similarly, a relationship between the values of the matrix and the corresponding coordinate frame the matrix represents (which is not always "world space," I should note). The upper-left 3x3 columns (or rows) represent the X, Y and Z axes of the coordinate frame.

Whether or not the rows represent axes or the column do depends on whether you are using the convention of multiplying as row vector * matrix or matrix times column vector. When performing matrix multiplication, the inner dimensions of the two matrices must agree, and so whether you are representing vectors as row matrices or column matrices impacts that choice (OpenGL and traditional math tend to prefer column vectors).

I recommend getting a good book on linear algebra, or at least taking a look at the Matrix and Quaternion FAQ and this post on matrix layouts in DirectX and OpenGL.